Group sparse regression has been well considered in multivariate linear models with appropriate relaxation schemes for the involved ${\ell }_{2,0}$-norm penalty. Lacking of the extended research on multivariate generalized linear models (GLMs), this paper targets at the original discontinuous and nonconvex ${\ell }_{2,0}$-norm based selection and estimation for multivariate GLMs. Under mild conditions, we give a necessary condition for selection consistency based on the notion of degree of separation, and propose the feature selection consistency as well as optimal coefficient estimation for the resulting ${\ell }_{2,0}$-likelihood estimators in terms of the Hellinger risk. Numerical studies on synthetic data and a real data in chemometrics confirm superior performance of the ${\ell }_{2,0}$-likelihood methods.

组稀疏回归在多元线性模型中得到了很好的考虑，其中包含适当的松弛方案。 ${\ell }_{2,0}$- 标准惩罚。缺乏对多元广义线性模型（GLMs）的扩展研究，本文针对原始的不连续和非凸${\ell }_{2,0}$-多变量 GLM 的基于范数的选择和估计。在温和条件下，我们基于分离度的概念给出了选择一致性的必要条件，并提出了特征选择一致性以及由此产生的最优系数估计。${\ell }_{2,0}$-Hellinger 风险方面的似然估计量。对合成数据和化学计量学中的真实数据的数值研究证实了${\ell }_{2,0}$- 似然方法。